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By Cyril Wells, Robert F. Mehl

THE practical importance of a knowledge of the rates of diffusion of carbon and of alloying elements in steel has often been pointed out 1,13 This importance ties chiefly, though by no means only, in the study of carburizing and in the study of reactions involved in the eutectoid inversion in steel The present paper is one of a series in which the rates of diffusion of carbon and of alloying elements in y-Fe and their mutual effects are measured with precision The present paper reports the results of meas¬urements of diffusion coefficients D of manganese in -y-Fe over wide ranges of temperature, and concentration, and of the effect of carbon and impurities and of grain size upon these diffusion coefficients [$] Data on the rate of diffusion of manganese in y-Fe have been reported by Fry2 and by Paschke and Hauttmann 3 Claussen4 calculated the diffusion coefficient D from Fry's data as 3 X 10-10 sq cm per sec at 960°, which will be shown to be incorrect by many orders of magnitude Paschke and Hauttmann gave a rough value of 9 6 X 10-8 sq cm per sec at 1400° Neither of these workers considered the variation of D with concentration and with temperature, and neither studied the effect of carbon METHOD AND MATERIALS Method -The method employed is identical with that used earlier 5 Owing to the volatility of manganese and the consequent loss of manganese from the outer surfaces of the welded diffusion bars, these surfaces were discarded The diffusion anneals were performed in argon, except one (test 18) in which hydrogen was employed for purposes noted below The temperatures reported are accurate to about 3° and constant within I°C , the diffusion times are reported to the nearest half hour The specimens were furnace-cooled after the diffusion anneal at about 2° per min Layers, usually 0 004 in thick, parallel to the welded interface, were machined from the specimens after the diffusion anneal and analyzed for manganese to 0 01 per cent Mn, the distances of these layers from the interface was measured to ±0 0002 in The concentration-penetration curves obtained were analyzed by both the Grube and the Matano solutions e The D values calculated by these two methods do not differ appreciably 5 The Grube solution was used except in tests in which the effect of concentration upon D was greater than 50 per cent, in such cases the Matano method, which explicitly provides for the variation of D with concentration,1 is the more reliable In general, the number of layers machined from the zones of variable composition were large enough to permit the use of the average layer composition as that of the center of the layer In 3 of the 30 tests, however, this is not justified, and the D values

Jan 1, 1941

By Cyril Wells, Robert F. Mehl

THE two earlier papers in this series1,2 presented data on the rate of diffusion of carbon and of manganese in gamma iron. Apart from their scientific interest, these [] data are needed chiefly in order to treat data on carburization, on the rate of formation of pearlite, and on the rate of austenizing in a quantitative way. 1,2,9,10 In the present investigation rates of diffusion of nickel in -?-Fe over wide temperature and concentration ranges have been determined, and the effects of carbon, of impurities, and of grain size on these rates have been studied. Claussen,3 using the data of Fry,4 has calculated the diffusion coefficient of nickel [ ] in -?-Fe as 9.2 X 10-11 sq. cm. per sec. at 1200T., but had no data from which to calculate the variation of D with concentration, temperature, and percentage of carbon. METHOD AND MATERIALS Method.-Nickel was diffused along the axis of a cylindrical specimen across a concentration gradient, concentration-penetration curves were determined and D values calculated from Grube or Matano solutions.5 Details of the method are given

Jan 1, 1941

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained-the isothermal growth of the phase follows a simple parabolic equation: [1 = ki [I]] where X is the thickness of the alloy layer, k the reaction rate constant, and [t] the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation: [k = Ae-QIRT [2]] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [I] where X is the thickness of the alloy layer, k the reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such. a plot has been con¬sidered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative, thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase .4 The reaction layers tend to have a

Jan 1, 1942

By Frederick C. Hull, Robert F. Mehl, Robert A. Colton

IT is known that pearlite forms from austenite by a process of nucleation and growth, and that the rate of formation of pearlite may be described by a rate of nucleation and a rate of growth 12 The manner in which these two quantities operate to produce the observed isothermal reaction curve has been analyzed in a paper published in 1939 3 Two types of process were described (I) that in which nucleation occurs at the grain boundaries of the parent phase, with the nodules growing toward the centers of the grains, initially as hemispheres and then after impingement as roughly radial-columnar structures, and (2) that in which nucleation occurs generally, with the nodules growing to full spheres until impingement with other growing nodules restricts growth Both cases are met in the formation of pearlite from austenite (Fig 1),2,3 the former, occurring near the knee of the S-curve has been named "grain-boundary transformation," and the latter, occurring at temperatures near AeI, has been named "group-nodule transformation " In developing our knowledge of the factors that determine the rate of formation of pearlite from austenite, it is important''' to obtain data on the rate of nucleation and the rate of growth of pearlite Such data, when obtained near the knee of the S-curve, will furnish information of use in understanding the actors that affect hardenability, when obtained at higher temperatures, such data will be useful in understanding the behavior of steels that during heat-treatment react to pearlite 2 It is the purpose of this paper to present data on the rate of nucleation and the rate of growth of pearlite in dependence upon composition, grain size, temperature,, and the degree of homogeneity of the parent austenite The studies are restricted chiefly to plain carbon commercial steels PREVIOUS DATA ON RAID OF NUCLEATION AND RATE OF GROWTH Data on the rate of nucleation and the rate of growth of pearlite have been published by Scheil and Lange-Weise,5 by Mirkin and Blanter,6,7 by Mehl,1 and by Dorn, De Garmo and Flanigan22 It is difficult to interpret the data, for in most cases too little information is given on austenitizing temperatures and times, the state of homogeneity of the austenite (presence or absence of carbide, etc ), austenite grain size, and mode of formation of pearlite at the temperatures given

Jan 1, 1942

By Frederick C. Hull, Robert F. Mehl, Robert A. Colton

IT is known that pearlite forms from austenite by a process of nucleation and growth, and that the rate of formation of pearlite may be described by a rate of nucleation and a rate of growth.1,2 The manner in which these two quantities operate to produce the observed isothermal reaction curve has been analyzed in a paper published in 1939.3 Two types of process were described: (1) that in which nucleation occurs at the grain boundaries of the parent phase, with the nodules growing toward the centers of the grains, initially as hemi¬spheres and then after impingement as roughly radial-columnar structures; and (2) that in which nucleation occurs generally, with the nodules growing to full spheres until impingement with other growing nodules restricts growth. Both cases are met in the formation of pearlite from austenite (Fig. 1);2.4 the former, occurring near the knee of the S-curve has been named "grain-boundary transformation," and the latter, occurring at temperatures near Ae1, has been named "group-nodule transformation." In developing our knowledge of the factors that determine the rate of formation of pearlite from austenite, it is important 1,2 to obtain data on the rate of nucleation and the rate of growth of pearlite. Such data, when obtained near the knee of the S-curve, will furnish information of use in understanding the factors that affect hardenability; when obtained at higher temperatures, such data will be useful in understanding the behavior of steels that during heat-treatment react to pearlite.2 It is the purpose of this paper to present data on the rate of nucleation and the rate of growth of pearlite in dependence upon composition, grain size, temperature, and the degree of homogeneity of the parent austenite. The studies are restricted chiefly to plain carbon commercial steels.* PREVIOUS DATA ON RATE OF NUCLEATION AND RATE OF GROWTH Data on the rate of nucleation and the rate of growth of pearlite have been published by Scheil and Lange-Weise,5 by Mirkin and Blanter,6,7 by Mehl,1 and by Dorn, De Garmo and Flanigan.2 It is difficult to interpret the data, for in most cases too little information is given on austenitizing temperatures and times, the state of homogeneity of the austenite (presence or absence of carbide, etc.), austenite grain size, and mode of formation of pearlite at the temperatures given.

Jan 1, 1942

By Curtis Wilson

FROM the results of his investigation of the hardenable copper-nickel-silicon and copper-cobalt-silicon alloys, M. G. Corson1 explained the dispersion-hardening effect by assuming the precipitation of the inter-metallic compounds nickel silicide and cobalt silicide, and on this basis he constructed diagrams for the pseudobinary systems copper-nickel silicide and copper-cobalt silicide. A consideration of these diagrams and of the factors that exert such an important influence upon the rate of precipitation, such as degree of supersaturation, nucleus number and rate of diffusion, leads to the expectation that the rate of precipitation of the silicides on reheating the quenched solid solutions at temperatures below the alpha-phase boundary should increase continuously as the reheating temperature is raised. The present investigation shows that while this rate does increase with the reheating temperature in a general way, it does not do so continuously. Supplements to Corson's diagrams are offered, showing the discontinuities, and slight modifications in the solubility curves are suggested.

Jan 1, 1933

By Lawrence K. Jetter, Robert F. Mehl

SOME advances have been made recently in the theory of the kinetics of precipitation from metallic solid solution despite the complexities of the problem, but there is surprisingly little quantitative information available on rates of precipitation with which to test present theory or upon which to build new theory.‡ Attempts to measure rates of precipitation have been beset with difficulties which originate both in the anomalies that attend the changes in the properties selected for measurement, as, for example, in electrical conductivity or mechanical properties, and also in the complexities in the structural changes in some systems, as in the aluminum-copper system. If the functional relationship between the quantity of precipitate and the value of the selected property is uncertain, measurements of that property are obviously of uncertain utility in determining absolute rates of precipitation. If the precipitating system passes through one or more transition stages, the interpretation of measured rates lacks definiteness; in such cases, it is necessary to measure the rate of reaction in each separate stage, if the rate measurements are to have any significance from the kinetic point of view.* These difficulties cannot be wholly avoided, for at least in some measure they are characteristic of the process of precipitation from solid solution, but they can be minimized both by the selection of a simple system and by the use of a method of measurement relatively free from anomalous behavior. The present paper reports dilatometric measurements on the rate of precipitation of silicon from the aluminum-rich solid solution in the aluminum-silicon system-a study that approaches the desiderata of simplicity. The aluminum-silicon system offers advantages from these points of view: there are no known anomalies in the property changes accompanying precipitation; 2.3,4 there are no known transition stages; the precipitate is an element, not a compound, and both matrix and precipitate are cubic, and while the structures are not identical (the solid solution is face-centered cubic and the precipitate is diamond cubic), the system at least approaches the ideal case of a crystal precipitating from a matrix of the same crystal type-the ideal case which Becker5 assumed in treating the precipitation process theoretically. The dilatometric method, while not free from disturbing effects, as the subsequent dis-

Jan 1, 1942

By Lawrence K. Jetter, Robert F. Mehl

SOME advances have been made recently in the theory of the kinetics of precipitation from metallic solid solution despite the complexities of the problem, but there is surprisingly little quantitative information available on rates of precipitation with which to test present theory or upon which to build new theory.? Attempts to measure rates of precipitation have been beset with difficulties which originate both in the anomalies that attend the changes in the properties selected for measurement, as, for example, in electrical conductivity or mechanical properties, and also in the complexities in the structural changes in some systems, as in the aluminum-copper system. If the functional relationship between the quantity of precipitate and the value of the selected property is uncertain, measurements of that property are obviously of uncertain utility in determining absolute rates of precipitation. If the precipitating system passes through one or more transition stages, the interpretation of measured rates lacks definiteness; in such cases, it is necessary to measure the rate of reaction in each separate stage, if the rate measurements are to have any significance from the kinetic point of view.* These difficulties cannot be wholly avoided, for at least in some measure they are characteristic of the process of precipitation from solid solution, but they can be minimized both by the selection of a simple system and by the use of a method of measurement relatively free from anomalous behavior. The present paper reports dilatometric measurements on the rate of precipitation of silicon from the aluminum-rich solid solution in the aluminum-silicon system-a study that approaches the desiderata of simplicity. The aluminum-silicon system offers advantages from these points of view: there are no known anomalies in the property changes accompanying precipitation ;2,3,4 there are no known transition stages; the precipitate is an element, not a compound, and both matrix and precipitate are cubic, and while the structures are not identical (the solid solution is face-centered cubic and the precipitate is diamond cubic), the system at least approaches the ideal case of a crystal precipitating from a matrix of the same crystal type-the ideal case which Becker5 assumed in treating the precipitation process theoretically. The dilatometric method, while not free from disturbing effects, as the subsequent dis-

Jan 1, 1942

By John R. Lewis

DURING the past few years there has been considerable interest in the sizing and the preparation of the iron ore fed into blast furnaces. Furnacemen know that proper sizing of ore tends to increase the efficiency of the furnace. It has been shown by Joseph1 and his associates that there is a direct relationship between the porosity of an ore particle and the time required for its reduction in the blast furnace. This relationship may be stated as follows: All other factors remaining constant, the time for reduction of a given sample of ore is inversely proportional to its porosity. As a consequence, large pieces of very porous ore, say 3 or 4 in. in cross section, will be completely reduced by the time they reach the hot zone just above the tuyeres, while large pieces of dense, nonporous ore may reach the hot zone with their centers unreduced. This means that for the latter complete reduction will be accomplished by the so-called "direct method;" i.e., where carbon reacts directly with the ore. Some recent work by Philbrook2 seems to contradict this rule. He found that of two unlike ores he studied, the one with the lower porosity reduced more readily. He explained his results as "possibly due to an apparently greater tendency of the `A' ore (lower porosity) to crack during preliminary dehydration and during reduction." This brings his results in line with the rule stated above. It is not the author's intention to enter into a discussion of the merits of "direct" versus "indirect" reduction. It is enough to say that, in general, indirect reduction is desirable. For the greatest efficiency, Gruner's theorem3 requires that all reduction in the blast furnace be indirect. Joseph seems to believe this also, because in his recent article on Some Comparisons between Iron Ore, Sinter and Nodules as Blast Furnace Feed' he concludes that: "In general, the carbon in blast-furnace coke is used most efficiently when the largest amount of the carbon charged reaches the tuyeres." However, P. V. Martin,' in an excellent paper, has shown that some direct reduction may actually increase the efficiency of the furnace; that is, increase its rate of production while maintaining maximum fuel economy. For nonporous ores there is more opportunity to have an excess of direct reduction unless the factors that make for indirect reduction are favored; for instance; the proper sizing of the ore particles. Another factor that has an important bearing on the reduction rate, as it is affected by particle size, is the flow of heat into the particle. The ore particle

Jan 1, 1947

By John Chipman

IN the manufacture of rimming steel-which constitutes the bulk of the world's production of mild steel-the factors that determine the quality of the product are very closely associated with the pouring and solidification of the steel in the ingot mold. The behavior of the metal in the mold is, on the one hand, the resultant of the complex processes through which the liquid metal has passed, and, on the other, it is an indication of the probable behavior of the ingot during subsequent rolling and finishing operations. A detailed study of the mechanism of solidifica-tion of rimming ingots ought to yield information that will be useful iii controlling the structure of the ingot and the quality of the ultimate product. The first step in such a study is to determine the rate at which the solid shell of the ingot forms from the liquid metal in the mold. A knowledge of the rate of solidification will make it possible to correlate observations of rimming action and gas evolution with studies of the structure, porosity, and segregation within the ingot. Thus, if the metal in the mold is observed to fall, let us say one minute after pouring, the portion of the structure associated with this fall will lie located in the part of the ingot that is solidifying at that particular moment. The knowledge that the ingot solidifies to a depth of ¾ in. in the first minute enables us to locate in the ingot the structural features corresponding to the observed fall. Conversely, the blowhole condition associated with a rising or growing ingot will be found in the part of the ingot that is solidifying at the time the phenomenon occurs. The time required for the complete solidification of an ingot has long been a matter of speculation. It is of considerable practical importance in connection with charging and heating in the soaking pits. Too rapid handling of the ingot through heating and rolling processes has been thought to be associated-with excessive pipe and other internal defects, so that a further object of this investigation was to attempt to estimate the time required for complete solidification, or the minimum practical time within which the subsequent operations can be performed with the minimum hazard.

Jan 1, 1937

By Frederick N. Rhines, Robert F. Mehl

IT has been shown elsewhere1 that the data on the rates of diffusion in solid metals are fragmentary and in many cases unacceptable. As a result, relatively little is known concerning the factors determining rates of diffusion and the variations in these rates with temperature. The first form of Fick's law (equation 1 below), ‡ in which the diffusion coefficient D is assumed invariant with composition, has been recognized for many years as only an approximation. The differential equation representing the second form of Fick's law (equation 4 below) has only recently been integrated by Matano,2 and unfortunately only in cases where a full diffusion-penetration curve (concentration-distance curve) has been obtained can the Matano solution be applied. The proper analysis of diffusion data is thus confined to the data of Grube and Zedele and of Zedele.§ These data are essentially for one temperature alone and do not furnish any information on the variation of the activation heat of diffusion, Q, with concentration: no information exists on the variation of Q with concentration within a singles olid solution field. 11 Much of the argument concerning the properties of metals that determine D and Q has been drawn from data in which variations of the quantities with concentration are unknown, for these data have been taken from experiments that could not furnish this information. Speculation concerning the properties of metals that may be effective in determining D and Q on the basis of data in which the chosen D and Q values are averages over wide concentration ranges of values at particular concentrations, ranges often of 100 per cent, is likely not to be fruitful.

Jan 1, 1938

By Frederick Rhines

IT has been shown elsewhere1 that the data on the rates of diffusion in solid metals are fragmentary and in many cases unacceptable. As a result, relatively little is known concerning the factors determining rates of diffusion and the variations in these rates with temperature. The first form of Fick's law (equation 1 below), ? in which the diffusion coefficient D is assumed invariant with composition, has been recognized for many years as only an approximation. The differential equation representing the second form of Fick's law (equation 4 below) has only recently been integrated by Matano,2 and unfortunately only in cases where a full diffusion-penetration curve (concentration-distance curve) has been obtained can the Matano solution be applied. The proper analysis of diffusion data is thus confined to the data of Grube and Jedele and of Jedele.§ These data are essentially for one temperature alone and do not furnish any information on the variation of the activa-tion heat of diffusion, Q, with concentration: no information exists on the variation of Q with concentration within a singles olid solution field. Much of the argument concerning the properties of metals that deter-mine D and Q has been drawn from data in which variations of the quan-tities with concentration are unknown, for these data- have been taken from experiments that could not furnish this information. Speculation concerning the properties of metals that may be effective in determining D and Q on the basis of data in which the chosen D and Q values are averages over wide concentration ranges of values at particular concen-trations, ranges often of 100 per cent, is likely not to be fruitful.

Jan 1, 1938

By Lars Thomassen, Ernest Kirkendall, Clair Upthegrove

THE amount of research done in the last few years on the subject of diffusion in solid metals is significant of the importance of this problem. To review the literature dealing with diffusion is unnecessary here. Desch1 in 1912 reviewed the work that had been done on diffusion in solids and gave a bibliography of the literature published before that time. Mehl's paper in 19362 is an excellent review of diffusion in metals and contains a large bibliography. Of importance also for its review and bibliography is an article by A. I. Krynitsky.3 While considerable material has appeared in the literature on diffusion in brass, the amount of information is not great compared to that pertaining to some of the other alloys. Most of the information published is of a qualitative nature; that which is quantitative varies considerably. Thus the quantitative determination of the rates of diffusion of copper and zinc in alpha brass by a new method appeared worth while. In the present investigation the rate of diffusion of zinc in approximately the same composition alpha brass has been determined at three temperatures. PROCEDURE The method used consisted of plating copper on a beta brass, heating it to allow diffusion to take place, and measuring the concentration of copper by determining the lattice constant of the alloy. This method is unique in that it uses a beta brass of such a composition that at the temperature at which diffusion takes place the beta brass is saturated with copper. Thus, while the beta brass supplies the zinc, no diffusion takes

Jan 1, 1938

By Ernest Kirkendall

THE amount of research done in the last few years on the subject of diffusion in solid metals is significant of the importance of this problem. To review the literature dealing with diffusion is unnecessary here. Desch1 in 1912 reviewed the work that had been done on diffusion in solids and gave a bibliography of the literature published before that time. Mehl's paper in 1936 2 is an excellent review of diffusion in metals and contains a large bibliography. Of importance also for its review and bibliography is an article by A. I. Krynitsky.3 While considerable material has appeared in the literature on diffusion in brass, the amount of information is not great compared to that pertain-ing to some of the other alloys. Most of the information published is of a qualitative nature; that which is quantitative varies considerably. Thus the quantitative determination of the rates of diffusion of copper and zinc in alpha brass by a new method appeared worth while. In the present investigation the rate of diffusion of zinc in approxi-mately the same composition alpha brass has been determined at three temperatures.

Jan 1, 1938

By T. E. Leontis, F. N. Rhines

THE oxide scale that forms upon magnesium at elevated temperatures is nonprotective in the sense that the rate of oxidation is constant and thus does not decrease with the growth of the scale as it does with other common metals. This generality was first stated by Pilling and Bedworth1 and has been verified by Suzuki2 and by Scheil.3 Pilling and Bedworth argued that the nonprotective characteristic could be predicted from the fact that magnesium oxide occupies less space than does the metal from which it springs, wherefore the scale is not expected to cover the metal so completely as to exclude all direct access to the atmosphere. Linear oxidation is thought by Scheil to be common to all cases where the reaction occurs at the oxide-metal interface. According to Suzuki,2 the product of high-temperature oxidation in the air is MgO contaminated with no more than traces of a nitride. When the metal is allowed to burn freely a fume composed of cubic crystals of Mg04 is given off. Delavault5 observed that excrescences form upon liquid magnesium and alloys in the course of oxidation. Beyond this it is known that the use of atmospheres containing small quantities of sulphur dioxide6 or carbon dioxide serve to retard the oxidation of solid magnesium and that beryllium7and calcium8 minimize the oxidation of molten magnesium exposed to the air. Many studies have been devoted to the nature and rates of "protective" oxidation, as exemplified by the cases of copper and iron, wherein the rate is characteristically parabolic. The theory of parabolic oxidation is well developed.9 Linear oxidation, on the other hand, has received but little attention and the theories proposed by Pilling and Bedworth and by Scheil have yet to withstand careful examination. There exists no comprehensive survey of the high-temperature oxidation of magnesium (or of any other metal that exhibits linear oxidation) over a broad range of temperature, under a variety of atmospheric conditions and covering a large group of alloys. It has been the purpose of the present investigation to provide such a survey, with the object of gaining a fuller understanding of linear oxidation, especially as applied to magnesium. EXPERIMENTAL PROCEDURE AND RESULTS The experimental studies undertaken were of two kinds: (I) measurement of the rate of oxidation as influenced by the

Jan 1, 1946

By W. A. Anderson, F. N. Rhines, W. A. Johnson

THE rate of the high-temperature oxidation of pure copper has been measured repeatedly by numerous investigators. It appears to be generally agreed: (I) that at constant temperature, after the initial stages of oxidation have been passed and the scale has attained a substantial depth, the film thickness increases in proportion to the square root of the time of oxidation; and (2) that for any given period of oxidation the logarithm of the square of the film thickness is proportional to the reciprocal of the absolute temperature of oxidation.' These relationships are explained upon the basis that the rate of diffusion of copper to the external surface of the film is the controlling factor in establishing the rate of growth. Extensive studies have been devoted also to the mechanism and rates of the early stages of oxidation. There is thus available a reasonably well established theory of the oxidation of pure copper upon which to construct an explanation of the more complex oxidation of copper alloys. Few general principles have as yet emerged from the chaos of observations that have been reported in the field of the oxidation of alloys.2 It is evident, however, that the copper alloys may be divided into two main groups, whose oxidation characteristics are distinguish able. The first group, composed of the alloys with the noble metals, forms substantially pure copper oxide scales; the alloying element is concentrated within the residual metal, and sometimes particles of almost pure noble metal are found in the scales completely surrounded by copper oxide. In the second group, composed of the alloys of copper with the baser metals, the alloying element appears as an oxide in the scale, often in greater concentration than in the alloy itself and sometimes to the exclusion of copper oxide. The oxide scales of the latter class have been found to be made up of one, two, and sometimes more distinguishable layers of which the innermost is often metallic in character, composed of particles of the oxide of the alloying element embedded in essentially pure copper and known as the subscale or zone of internal oxidation. The need for a thorough quantitative study of these modes of oxidation is evident. Since it is apparent that several mechanisms must be cooperating to produce the complex oxide scales found on copper alloys, the analysis of the process into its several simple operations should prove instructive. Fortunately, it is possible experimentally to produce internal oxidation in the absence of an external scale; this permits the isolation and intensive study of one of the steps in the oxidation process. In the present research the rates of internal oxidation of an extensive series of dilute solid solution alloys of copper have been measured and a theory has been developed to predict the observed

Jan 1, 1941

THE problem of reaction rates in the open-hearth process is essentially that of trying to form a fairly clear picture of the "chemical mechanisms" in the bath. Quantitative data on reaction rates would perhaps not be of much practical importance even if they were available; however, what few approximate data there are can be used in combination with data given in Chapters 16 and 17 to sketch a picture of the "chemical mechanics" of the open-hearth process that is consistent with essentially all the present available evidence. The result may later be found incorrect in many details but even so it will illustrate certain useful methods for obtaining a clearer understanding of the process. Consistent with the treatment in Chapter 15, but in simpler terms, we may say that chemical reactions in general involve the following elements or steps: 1. The reacting molecules are mixed together in space in such fashion as to favor collisions among them. 2. Units of what is usually an intermediate molecular arrangement called an activated complex are formed at a certain rate, depending on temperature and concentrations. 3. These activated complex units decompose into the reaction products (this step usually assumed to be so rapid as never to limit the over-all process). 4. In any of these steps, heat energy may have to flow into, or away from, the reaction zone to permit the reaction to proceed. 5. The products of reaction will usually have to move out of the way to permit further reaction. The temperature factor enters mainly through step 2, and its effect is very marked. (What is called temperature is really the mean energy content of all the molecules of the substance involved; at any one temperature a certain proportion of the moleculea will have much higher energy content than the mean value.) Various reaction rates measured at around room tem-

Jan 1, 1951

THE problem of reaction rates in the open-hearth process is essentially that of trying to form a fairly clear picture of the "chemical mechanisms" in the bath. Quantitative data on reaction rates would perhaps not be of much practical importance even if they were available; however, what few approximate data there are can be used in combination with data given in Chapters 16 and 17 to sketch a picture of the "chemical mechanics" of the open-hearth process that is consistent with essentially all the present available evidence. The result may later be found incorrect in many details but even so it will illustrate certain useful methods for obtaining a clearer understanding of the process. Consistent with the treatment in Chapter 15, but in simpler terms, we may say that chemical reactions in general involve the following elements or steps : 1. The reacting molecules are mixed together in space in such fashion as to favor collisions among them. 2. Units of what is usually an intermediate molecular arrangement called an activated complex are formed at a certain rate, depending on temperature and concentrations. 3. .These activated complex units decompose into the reaction products (this step usually assumed to be so rapid as never to limit the over-all process). 4. In any of these steps, heat energy may have to flow into, or away from, the reaction zone to permit the reaction to proceed. 5. The products of reaction will usually have to move out of the way to permit further reaction. The temperature factor enters mainly through step 2, and its effect is very marked. (What is called temperature is really the mean energy content of all the molecules of the substance involved; at any one temperature a certain proportion of the molecules will have much higher energy content than the mean value.) Various reaction rates measured at around room tem-

Jan 1, 1964

By G. B. Richardson

WHILE examining a number of curves showing the production of petroleum, the author was impressed by the rather uniform relationship between the cumulative production from the beginning of development FIG. I.-ACTUAL' AND COMPUTED PRODUCTION OF PETROLEUM IN WEST VIRGINIA. down to the time the peak was attained and the estimated total production. The curves examined showed an average ratio of cumulative peak production1 to total production of approximately 30 per cent. FIG. 2.-ACTUAL AND COMPUTED PRODUCTION OF PETROLEUM IN CAT CREEK FIELD, MONTANA. These relations were discussed with C. E. Van Orstrand, geophysicist of the Geological Survey, who investigated the subject mathematically.

Jan 3, 1925